Question

Sanjay takes a personal loan of ₹6,00,000 at the rate of 12% per annum for 'n' years. The EMI using the flat rate method is ₹16,000. The value of 'n' is:

• A. 3
• B. 6
• C. 5
• D. 4

Answer 1

The Correct Option is C

Solution: The flat-rate EMI is calculated using the formula:

\[EMI = \frac{Loan Amount + Total Interest}{Number of Months}\]

Total interest calculation The total interest under the flat rate method is:

\[Total Interest = Loan Amount \times Rate of Interest \times Time (in years)\]

Here, the loan amount is 6,00,000, the rate of interest is 12% = 0.12, and the time is \(n\) years. So:

\[Total Interest = 6,00,000 \times 0.12 \times n = 72,000 \times n\]

EMI calculation The EMI formula becomes:

\[16,000 = \frac{6,00,000 + 72,000n}{12n}\]

Multiply through by 12n to eliminate the denominator:

\[16,000 \times 12n = 6,00,000 + 72,000n\]

\[1,92,000n = 6,00,000 + 72,000n\]

Simplify:

\[1,92,000n - 72,000n = 6,00,000\]

\[1,20,000n = 6,00,000\]

Solve for n:

\[n = \frac{6,00,000}{1,20,000} = 5\]

Final Answer: The value of n is: \(5\)